Literally meaning unenthusiastic and unexcited, it is generally used when you don't want to do a certain activity or action.
Use this to completely shut down a person's request. Just continue saying 'Not Keen' to all their plea's, until they get bored and stop bothering you.
OR Friend: Be my wingman at this party, old mate.
Me: No Way! Not Keen.
OR Friend: Pass me my wallet.
Me: Nup, Not Keen.
OR (Rare situation) Friend: Smoke another billy man.
Me: Not Keen.